Chapter 27, Problem 63A

A satellite TV company broadcasts its signals from its earthbound broadcast station to a satellite in geosynchronous orbit 36,000 km away and from there back to Earth’s surface.

a. How much time elapses between the time the signal leaves the station and the time it is received by someone’s satellite dish?

b. Explain why the answer doesn’t depend very much on exactly where the TV company and the customer are located on Earth.

To determine

To determine the time elapses between the time the signal leaves the station and the time received by someone’s satellite dish.

Answer to Problem 63A

The time elapse is 0.24s.

Explanation of Solution

Given data:

The length of signal is 2×36,000 Km = 72,000 Km = 72,000×1000 m.

Formula used:

Time elapsed, $t=\frac{l}{c}$ s.

Calculation:

We know that, the speed of light c =3×10⁸m/s.

Substituting the values in the equation of time t is, $=\frac{72000\times 1000m}{3\times {10}^{8}m/s}$ s.

= 0.24 s.

The satellites boost the signal and send it back down to Earth from its transmitter to the receiver on the Earth. This process happens using radio waves, which travel at the same speed of light. So, it takes usually very little time for a few milliseconds only.

Conclusion:

The time elapse is 0.24seconds.

To determine

The time 0.24 seconds does not very much depend on the TV company and the customer.

Explanation of Solution

Introduction:

From the satellite link, the radio signal travels at 1.12×10⁸ m to get the signal from the TV company to the customer. The light travels at 3×10⁸m/s and we can notice half the second delay.

The Radio/TV signals are just small amounts of electricity that are at the right frequencies can travel in a usable footprint form the satellite. All the customers are within the footprint area of the company. The angle of the beam back to earth from the satellite will not be very large. The maximum angle is within the footprint area so the path is not large. This makes the signals transmit very efficiently. So, the time is not very much considerable.

Conclusion:

The delay in time for the radio signal is very small and does not depend on the TV company and the customer on the Earth.